document.write( "Question 299160: a plane flew 500 km from atlanta to louisville. when returning to atlanta the flight took 1/2 hour less time.if the rate to Louisville was 50km/hr faster than the rate returning, find the two rates in km/hr. \n" ); document.write( "

Algebra.Com's Answer #854272 by ikleyn(53875) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "a plane flew 500 km from Atlanta to Louisville. when returning to Atlanta the flight took 1/2 hour less time.
\n" ); document.write( "if the rate to Louisville was 50km/hr faster than the rate returning, find the two rates in km/hr.
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\n" ); document.write( "\n" ); document.write( "After reading this problem and its solution in the post by @mananth, I have two notices.\r
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\n" ); document.write( "\n" ); document.write( "Firstly, the problem's formulation in the post is absurdist and self-contradictory.
\n" ); document.write( "Indeed, it says that the flight to Atlanta took 1/2 hour less time
\n" ); document.write( "and the rate to Louisville was 50 km/h faster than the rate returning.\r
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\n" ); document.write( "\n" ); document.write( "So, the problem's creator was so hurry that missed circumstances.\r
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\n" ); document.write( "\n" ); document.write( "I will edit the problem as it is shown below, to make sense from nonsense:\r
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document.write( "      A plane flew 500 km from Atlanta to Louisville. When returning to Atlanta the flight took 1/2 hour  time. \r\n" );
document.write( "      If the rate to Louisville was 50km/h faster than the rate returning, find the two rates in km/hr.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Secondly, in the post by @mananth, both the solution and the answer are incorrect due to arithmetic errors.\r
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\n" ); document.write( "\n" ); document.write( " I came to bring a correct solution to this my edited formulation.\r
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document.write( "Let the rate to Louisville be x km/h.\r\n" );
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document.write( "Time of this flight is    hours.\r\n" );
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document.write( "The rate to Atlanta (returning) will be (x-50) km/h.\r\n" );
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document.write( "The time of this returning flight is   hours.\r\n" );
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document.write( "Time equation is\r\n" );
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document.write( "     -  =   of an hour.   <<<---===  It says literally what the problem says\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    2*500*x - 2*500*(x-50) = x*(x-50),\r\n" );
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document.write( "    1000x - 1000x + 50000 = x^2 - 50x,\r\n" );
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document.write( "    x^2 - 50x + 50000 = 0,\r\n" );
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document.write( "    (x-250)*(x+200) = 0,\r\n" );
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document.write( "    x = 250  or  x = -200.\r\n" );
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document.write( "We choose the positive root and reject the negative one.\r\n" );
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document.write( "ANSWER.  The rate from Atlanta to Louisville was 250 km/h.  The rate of the returning trip from Louisville to Atlanta was 250-50 = 200 km/h.\r\n" );
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document.write( "CHECK.  The tome flying from Atlanta to Louisville was   = 2 hours.\r\n" );
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document.write( "        The time flying from Louisville to Atlanta (returning) was   = 2.5 hours, in 0.5 hours longer.\r\n" );
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document.write( "        Precisely correct.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The problem edited and converted from self-contradictory to self-consistent
\n" ); document.write( "and then solved in a right way.\r
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